Successful couplings for a class of stochastic differential equations driven by Lévy processes (Q1933988)

The authors consider a class of SDEs driven by Lévy processes. ``By constructing proper coupling operators for the integro-differential type Markov generator'', they prove the existence of a successful coupling for the processes under consideration. Applications include a result on ergodicity as well as the proof of a ``new Liouville theorem for space-time bounded harmonic functions with respect to the underlying Markov semigroups''. This result ``is sharp for Ornstein-Uhlenbeck processes driven by \(\alpha\)-stable Lévy processes''.